The US has no record of Cruz being born. Upon attempting to enter this country, he (or his mother on his behalf prior to his 18th Bday) must prove that he is an American through the legal processes of our nation.
The question that remains is, are you still considered natural born by having had to take those steps?
To date none of those legal documents have been presented publicly by Cruz in defense of this issue, not even his US passport. Somehow he has gotten from point A to point C and there is no evidence of all the very necessary point B requirements being fulfilled.
With that I agree. The McCain case comes to mind